On Countable Dense and Strong Local Homogeneity
Bulletin Polish Acad. Sci. Math. 53 (2005), 401-408 MSC: 57N20, 54G20. DOI: 10.4064/ba53-4-5
We present an example of a connected, Polish, countable dense homogeneous space $X$ that is not strongly locally homogeneous. In fact, a nontrivial homeomorphism of $X$ is the identity on no nonempty open subset of $X$.